xDSL modem having adaptive compensating filter of null generated by bridged tap

ABSTRACT

A xDSL modem having an adaptive compensating filter of null generated by BT (Bridged Tap) minimizes transmission errors. The VDSL having a null compensating filter comprises a null compensator for finding a null frequency generated on a transfer function of a receiving signal before the DFE by predicting and tracing the null frequency to enlarge a signal component of the null frequency. The damage of a signal component resulting from the null generated by BT on a subscriber line is previously compensated before the equalizer. As a result, degradation of transmission speed of xDSL service is prevented and the number of taps in the equalizer is reduced, thereby reducing cost in embodiment of hardware.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention generally relates to a high rate DigitalSubscriber Line (xDSL) modem, and more specifically, to a xDSL modemwith a Carrierless Amplitude and Phase modulation (hereinafter,abbreviated as “CAP”) or Quadrature Amplitude Modulation (hereinafter,abbreviated as “QAM”) method which is configured to install a digitalfilter in front of an equalizer therein, thereby minimizing transmissionerrors generated by Bridged Tap (hereinafter, abbreviated as “BT”) ofsubscriber lines.

[0003] 2. Description of the Prior Art

[0004] In a digital communication system, a transmission signal iseasily distorted by a band-limited channel characteristic while passingthrough a transmission channel. This distortion is generated by gaussnoise, thermal noise, impulse noise, additional or multiple noise due toa fading phenomenon where the strength of a signal varies depending ontime, frequency change, non-linearity and temporal dispersion.

[0005] Adjacent symbols in the transmission signal are affected by theabove-described distortion. This Inter-Symbol Interference (hereinafter,abbreviated as “ISI”) is a main cause to degrade performance of thecommunication system. Specifically, in a QAM system, the ISI isaggravated by multi-level characteristics, which results in obstacle tohigh-speed data communication.

[0006] The equalizer restores the transmission signal distorted by theISI.

[0007] Recently, many researches have been made to solve the ISI. Ofthese researches, a Decision Feedback Equalizer (hereinafter,abbreviated as “DFE”) is proved to have the most excellent performanceeven in inferior channel conditions.

[0008]FIG. 1 illustrates a general structure of a VDSL modem with aconventional QAM or CAP method.

[0009] A transmission signal inputted through a channel 1 is distortedby noise n(t) such as additional white noise (AWGN) resulting fromchannel characteristics. The transmission signal affected by the noisen(t) is converted into a digital signal by an A/D converter 2.

[0010] The transmission signal converted by the A/D converter 2 isapplied to a feed-forward filter (hereinafter, abbreviated as “FFF”) 3of the DFE comprising a Finite Impulse Response (hereinafter,abbreviated as “FIR”) with a predetermined cycle to remove a precursor,and then applied to an adder 4.

[0011] The transmission signal, which is outputted from the FFF 3 andapplied to the adder 4, is added with an output signal from a FeedbackFilter (hereinafter, abbreviated as “FBF”) 6, and applied to a signaldeterminer 5.

[0012] The signal determiner 5 receives an output signal from the adder4 to determine a level of the output signal.

[0013] The FBF 6 receives a value determined by the signal determiner 5to remove a post-cursor of the value, and outputs the value whosepost-cursor is removed into the adder 4.

[0014]FIG. 2 illustrates a structure of BT where a cable connected inparallel to a transmission channel is disconnected in a VDSL.

[0015] The BT generates null on a transfer function of the transmissionchannel.

[0016] A downward signal transmitted from a sending end 7 into asubscriber 8 is bridged in a bridged point B and reflected in across-section to be re-added in the bridged point B.

[0017] If a length of the BT is d, the transmission signal istransmitted by 2d through the BT. When a wavelength λ of a transmissionsignal satisfies d=λ/4 or 2d=λ/2, a phase difference of 180° occursbetween a transmission signal which is bridged and retraced and atransmission signal which is not bridged. As a result, the two signalscause destructive interference from each other to remove a predeterminedsignal based on a corresponding frequency.

[0018] In other words, a null is generated on a channel transferfunction as shown in FIG. 3 in a frequency having the wavelength A fourtimes longer than the BT,.

[0019] When a speed of a wave is v, the frequency f₀ of a first nullgenerated by the BT is expressed as follows. $\begin{matrix}{f_{0} = {{v/\lambda} = \frac{v}{4\quad d}}} & \text{[Equation~~1]}\end{matrix}$

[0020] Since the speed of the wave is determined by a medium, if thespeed of light is c and an insulation constant of the medium is ε_(r),Equation 1 is expressed as follows. $\begin{matrix}{f_{0} = {\frac{v}{4\quad d} = {\frac{c}{4d\sqrt{ɛ_{r}}} = \frac{K}{d}}}} & \text{[Equation~~2]}\end{matrix}$

[0021] Also, null is generated in the frequency of multiples of oddnumbers of the null frequency f₀, that is, in (2K+1)f₀. As the length dbecomes shorter, the depth of the null becomes deeper, therebydistorting the transmitted signal.

[0022] When the length of the channel is l, the channel transferfunction of the subscriber line is generally expressed as follows.

|H(f)|=e ^(−1α(f)) ≈e^(−1α{square root}{square root over (f)})  [Equation 3]

[0023] Here, α(f) which represents a reduction constant of the linegenerally varies in the square root of frequency.

[0024] The Equation 3 can be expressed as Equation 4 since l is areciprocating length 2d of the BT.

|H(f)|=e ^(−2dα(f)) ≈e^(−2dα{square root}{square root over (f)})  [Equation 4]

[0025] Since the first null frequency f₀=K/d, the transfer function ofthe BT in the null frequency f₀ can be represented as follows.

|H _(bt)(f)|=e^(−(2Kα/{square root}{square root over (f ₀ )}))  [Equation 5]

[0026] In Equation 5, if f₀ becomes larger infinitely, that is, if thelength of the BT becomes much shorter, the value of the transferfunction of the BT is closer to 1. As a result, the transmission signalfrom the sending end 7 is remarkably reduced at the BT point B. In otherwords, the shorter becomes the length of the BT, the larger null isgenerated in a channel, which results in increase of transmissionerrors.

[0027] In the VDSL with a CAP or QAM method, the distortion on thetransfer function is equalized by the DFE as shown in FIG. 1.

[0028] However, it is difficult to equalize deep null by a short BTunless the number of taps of the DFE is large. If the number of tapsincreases in order to solve this problem, the number of shift resistorsalso increases. As a result, hardware to the DFE becomes complicated,thereby increasing deciding delay time.

[0029] In addition, when the depth and width of the null are very large,it is difficult to minimize the transmission errors and to equalize thechannel transfer function using the DFE.

SUMMARY OF THE INVENTION

[0030] Accordingly, it is an object of the present invention topre-equalize a channel transfer function before an equalization processof a DFE by predicting null generated by a BT adaptively to compensate asignal component damaged by the null, thereby improving equalizationperformance.

[0031] In an embodiment, a xDSL (high rate Digital Subscriber Line)modem having a DFE (Decision Feedback Equalizer) comprises a nullcompensator for finding a null frequency generated on a transferfunction of a receiving signal before the DFE by predicting and tracingthe null frequency to compensate a signal component of the nullfrequency.

BRIEF DESCRIPTION OF THE DRAWINGS

[0032]FIG. 1 illustrates a general structure of a VDSL modem with aconventional QAM or CAP method.

[0033]FIG. 2 illustrates a structure of BT where a cable connected inparallel to a transmission channel is disconnected in a VDSL interval.

[0034]FIG. 3 illustrates generation of null in a transmission signal bya BT on a channel.

[0035]FIG. 4 illustrates a structure of a structure of a VDSL modemaccording to an embodiment of the present invention.

[0036]FIG. 5 illustrates a pole-zero diagram and a transfer function ofa null compensating filter according to an embodiment of the presentinvention.

[0037]FIGS. 6a to 6 c illustrates a power spectrum in trace of the nullbased on minimum average power of the null compensating filter accordingto an embodiment of the present invention.

[0038]FIG. 7 illustrates the change of average power of nullcompensating filter output depending on a predicting null frequency.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0039] The present invention will be described in detail with referenceto the accompanying drawings.

[0040]FIG. 4 illustrates a structure of a VDSL modem according to anembodiment of the present invention.

[0041] In an embodiment, a digital subscriber line modem comprises anull compensator 10 for adaptively predicting null generated by BT in aDFE (Decision Feedback Equalizer), tracing a position of the null andcompensating a signal component damaged by the null, therebypre-equalizing a channel transfer function before an equalizationprocess of the DFE.

[0042] The null compensator 10 comprises a null compensating filter 11having a transfer function with an inverse characteristic to the nullgenerated on the channel transfer function by the BT, and a null tracer12 for tracing a position of the null.

[0043] The null compensating filter 11 enlarges a signal component of anull frequency to compensate the null generated on the transfer functionof an applied signal channel.

[0044] The null compensating filter 11 has a transfer function with aninverse characteristic to a notch filter having a transfer functioncharacteristic with a notch type.

[0045] The null tracer 12 traces a position of the null generated on thechannel transfer function by the BT depending on null tracing algorithm,thereby fining a null frequency.

[0046] Here, the null tracer 12 predicts and traces the null frequencywith a RPE (Recursive Prediction Error) algorithm and a Gauss-Newtonmethod.

[0047] The rest elements of FIG. 4 are the same as those of FIG. 1except the null compensating filter 11 and the null tracer 12.

[0048] Since the null compensating filter 11 has a transfer functioncharacteristic of inversion relation with a notch filter having atransfer function characteristic with a notch type, a transfer functionof the null compensating filter 11 with an quadratic Infinite ImpulseResponse (hereinafter, abbreviated as “IIR”) type is expressed asfollows. $\begin{matrix}{\begin{matrix}{{H\left( z^{- 1} \right)} = \frac{W\left( {\alpha \quad r\quad z^{- 1}} \right)}{W\left( {r\quad z^{- 1}} \right)}} \\{= \frac{1 - {2\alpha \quad r\quad \cos \quad \theta \quad z^{- 1}} + {\alpha^{2}r^{2}z^{- 2}}}{1 - {2\quad r\quad \cos \quad \theta \quad z^{- 1}} + {r^{2}z^{- 2}}}} \\{{= \frac{1 + {\alpha \quad r\quad a\quad z^{- 1}} + {\alpha^{2}r^{2}z^{- 2}}}{1 + {r\quad a\quad z^{- 1}} + {r^{2}z^{- 2}}}},}\end{matrix}{{o < r < 1},{0 < \alpha < 1}}} & \text{[Equation~~6]}\end{matrix}$

[0049] Here, θ represents a null frequency by radian, r represents aradius of pole, and α represents a zero contraction coefficient.Specifically, the α determines a band width of a com-shaped spectrum.

[0050]FIG. 5 illustrates a pole-zero diagram and a transfer function ofthe null compensating filter 11 according to an embodiment of thepresent invention.

[0051] To compensate null on the channel transfer function generated bythe BT, a position of the null is adaptively predicted, and a signalcomponent of a corresponding frequency is to be enlarged with acorn-shaped transfer function as shown in FIG. 5.

[0052] For this operation, the null tracer 12 predicts the position ofthe null adaptively with an output power spectrum of the nullcompensating filter 11.

[0053] The adaptive prediction method of the null tracer 12 is asfollows.

[0054] A basic method of finding a null frequency in the null tracer 12is to predict a frequency having a minimum average power to an outpute(n) of the null compensating filter 11. An error gradient forpredicting the frequency is calculated with a RPE algorithm, and a nextprediction null frequency is repeatedly updated with a Gauss-Newtonmethod.

[0055] If the output of the null compensating filter 11 is e(n), theaverage power of the output e(n) is expressed as follows.$\begin{matrix}{V_{N} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}{e^{2}(n)}}}} & \text{[Equation~~7]}\end{matrix}$

[0056] Suppose that null is generated on a channel transfer function.When the prediction null frequency of the null compensating filter 11 isâ(n)=−2 cos{circumflex over (θ)}(n), if the prediction null frequencyâ(n) is different from the actual null frequency, the average power ofthe null compensating filter 11 increases due to the prediction nullfrequency â(n) by the null compensating filter 11.

[0057] On the other hand, as the prediction null frequency â(n) iscloser to the actual null frequency, the average power of the nullcompensating filter 11 becomes smaller gradually. When prediction nullfrequency â(n) is identical with the actual null frequency, the averagepower of the null compensating filter 11 becomes minimized.

[0058]FIGS. 6a to 6 c illustrates a power spectrum in trace of the nullbased on minimum average power of the null compensating filter 11according to an embodiment of the present invention.

[0059]FIGS. 6a and 6 b shows a pattern of Power Spectral Density(hereinafter, abbreviated as “PSD”) when the position of the null is notfound. FIG. 6c shows a pattern of PSD when the position of the null isexactly found to strengthen the signal component of the correspondingfrequency.

[0060] The average power is the same as integral calculus (∫_(−∞)^(∞)PSDdf) of PSD as shown in FIG. 6. AS a result, as the area of PSDbecomes larger, the average power increases.

[0061] Equation 6, the transfer function of the null compensating filter11, is expressed as follow by αr=δ. $\begin{matrix}{\begin{matrix}{{H\left( z^{- 1} \right)} = \frac{W\left( {\delta \quad z^{- 1}} \right)}{W\left( {r\quad z^{- 1}} \right)}} \\{= \frac{1 - {2\delta \quad \cos \quad \theta \quad z^{- 1}} + {\delta^{2}z^{- 2}}}{1 - {2\quad r\quad \cos \quad \theta \quad z^{- 1}} + {r^{2}z^{- 2}}}} \\{{= \frac{1 + {\delta \quad a\quad z^{- 1}} + {\delta^{2}z^{- 2}}}{1 + {r\quad a\quad z^{- 1}} + {r^{2}z^{- 2}}}},}\end{matrix}{{o < r < 1},{o < \delta < 1}}} & \text{[Equation~~8]}\end{matrix}$

[0062] If a transmission signal inputted into the null compensatingfilter 11 after sampled consecutively in an A/D converter 2 is y(n), theoutput e(n) of the null compensating filter 11 having theabove-described transfer function characteristic is expressed asfollows. $\begin{matrix}{{e(n)} = {{{H\left( {n,q^{- 1}} \right)}{y(n)}} = {\frac{1 + {\delta \quad {\hat{a}(n)}q^{- 1}} + {\delta^{2}q^{- 2}}}{1 + {r\quad {\hat{a}(n)}q^{- 1}} + {r^{2}q^{- 2}}}{y(n)}}}} & \text{[Equation~~9]}\end{matrix}$

[0063] Here, q⁻¹ represents a unit delay operator.

[0064] Equation 9 can be expressed with a difference equation type asfollows.

W(rq ⁻¹)e(n)=W(δq⁻¹)y(n)  [Equation 10]

(1+raq ⁻¹ +r ² q ⁻²)e(n)=(1+δαq ⁻¹ +δ ² q ⁻²)y(n)  [Equation 11]

e(n)+rae(n−1)+r ² e(n−2)=y(n)+δαy(n−1)+δ² y(n−2)  [Equation 12]

e(n)=−rae(n−1)−r ² e(n−2)+y(n)+δαy(n−1)+δ² y(n−2)  [Equation 13]

[0065] Here, Equation 10 differentiated to the frequency a can beexpressed as follows. $\begin{matrix}{{{{W\left( {r\quad q^{- 1}} \right)}\frac{\partial{e(n)}}{\partial a}} + {\frac{\partial{W\left( {rq}^{- 1} \right)}}{\partial a}{e(n)}}} = {{{W\left( {\delta \quad q^{- 1}} \right)}\frac{\partial{y(n)}}{\partial a}} + {\frac{\partial{W\left( {\delta \quad q^{- 1}} \right)}}{\partial a}{y(n)}}}} & \text{[Equation~~14]} \\{{{{W\left( {r\quad q^{- 1}} \right)}\frac{\partial{e(n)}}{\partial a}} + {\left( {r\quad q^{- 1}} \right){e(n)}}} = {{{W\left( {\delta \quad q^{- 1}} \right)}\frac{\partial{y(n)}}{\partial a}} + {\left( {\delta \quad q^{- 1}} \right){y(n)}}}} & \text{[Equation~~15]} \\{{{{W\left( {r\quad q^{- 1}} \right)}\frac{\partial{e(n)}}{\partial a}} + {{re}\left( {n - 1} \right)}} = {\delta \quad {y\left( {n - 1} \right)}}} & \text{[Equation~~16]} \\{{{W\left( {r\quad q^{- 1}} \right)}\frac{\partial{e(n)}}{\partial a}} = {{\delta \quad {y\left( {n - 1} \right)}} - {{re}\left( {n - 1} \right)}}} & \text{[Equation~~17]}\end{matrix}$

[0066] In Equation 15, since the input data y(n) has no relation withthe frequency α, $\frac{\partial{y(n)}}{\partial a} = 0.$

[0067] In order to reduce the output of the null compensating filter 11or decrease difference between the output of the null compensatingfilter 11 and prediction error, the next prediction null frequencyâ(n+1) to the initial prediction null frequency â(n) is required to movein a minus direction to $\frac{\partial{e(n)}}{\partial a}.$

[0068] Referring to FIG. 7, when the average power of the nullcompensating filter 11 having a quadratic function type has the only oneminimum point, the next prediction null frequency â(n+1) is required tomove in a minus direction to $\frac{\partial{e(n)}}{\partial a}$

[0069] so that the next prediction null frequency â(n+1) may move towardthe minimum point (f₀) of the average power.

[0070] If a minus prediction error gradient is defined as ψ(n), ψ(n) canbe expressed as follows. $\begin{matrix}{{\psi (n)} = {{- \frac{\partial{e(n)}}{\partial a}}_{a = {\hat{a}{(n)}}}}} & \left\lbrack {{Equation}\quad 18} \right\rbrack\end{matrix}$

[0071] Equation 17 is substituted in Equation 18 to obtain Equation 19.$\begin{matrix}\begin{matrix}{{\psi (n)} = {{- \frac{\partial{e(n)}}{\partial a}}_{a = {\hat{a}{(n)}}}}} \\{= \frac{{{- \delta}\quad {y\left( {n - 1} \right)}} + {r\quad {e\left( {n - 1} \right)}}}{W\left( {r\quad q^{- 1}} \right)}} \\{= \frac{{{- \delta}\quad {y\left( {n - 1} \right)}} + {r\quad {e\left( {n - 1} \right)}}}{1 + {r\quad a\quad q^{- 1}} + {r^{2}q^{- 2}}}}\end{matrix} & \left\lbrack {{Equation}\quad 19} \right\rbrack\end{matrix}$

[0072] If the current prediction frequency is â(ni) and the nextprediction null frequency is â(n+1), the next prediction null frequencyâ(n+1) according to the Gauss-Newton method is updated as shown inEquation 20.

{circumflex over (a)}(n+1)={circumflex over(a)}(n)+(1−ρ)R(n)⁻¹ψ(n)e(n)  [Equation 20]

[0073] Here, (1-ρ) as a parameter identical with a step sizerepresenting in a repeatedly updated equation limits a maximumfluctuation width of the prediction null frequency â. The value of (1-ρ)is determined at random depending on sensitivity to predictioncapability of the modem and noise.

[0074] To reduce dispersion of the prediction null frequency â, it ispreferable that the value of (1-ρ) is smaller. If the value of (1-ρ) isvery small, a convergence time to fine a position of the null becomeslonger. However, since the position of the null generated by the BT isnot change depending on time, rapid trace depending on time change isnot required. Therefore, it is preferable that the value of (1-ρ) issmall if possible.

[0075] R(n) represents a sum of square second-derivative, which isgenerally known for a “Gauss-Newton direction”. The Gauss-Newtondirection is represented as follows.

R(n)=R(n−1)+(1−ρ)(ψ(n)² −R(n−1))  [Equation 21]

[0076] The output e(n) of the null compensating filter 11 is actuallyembodied using Equation 13 instead of Equation 9.

[0077] As shown in FIG. 7, since there is the only one minimum point ofthe average power in the whole range of the prediction null frequency,the prediction null frequency of the null compensating filter 11 isconverged in the actual null frequency. As a result, the damage of thesignal component due to the null can be compensated.

[0078] The transmission signal compensated by the null compensatingfilter 11 is applied to the FFF 3 of the DFE. The subsequent process isidentical with the conventional process of the DFE.

[0079] As described above, in a VDSL modem having a null compensatoraccording to an embodiment of the present invention, damage of a signalcomponent resulting from null generated by BT on a subscriber line ispreviously compensated before an equalizer. As a result, our inventionenable the VDSL system to prevent degradation of transmission speed ofhigh speed Internet services and to reduce the number of taps of DFE,and thereby to reduce hardware cost.

What is claimed is: 1 A xDSL (Very high rate Digital Subscriber Line) modem having a DFE (Decision Feedback Equalizer), comprising a null compensator for finding a null frequency generated on a transfer function of a receiving signal before the DFE by predicting and tracing the null frequency to enlarge a signal component of the null frequency.
 2. The xDSL according to claim 1, wherein the null compensator comprises: a null compensating filter for enlarging the signal component corresponding to the null frequency on the transfer function of the receiving signal; and a null tracer for tracing the null frequency using minimum point of a average power or a output energy of the null compensating filter.
 3. The xDSL according to claim 2, wherein the null compensating filter has a transfer function with an inverse characteristic to a notch filter having a transfer function characteristic with a notch type.
 4. The xDSL according to claim 2, wherein the null tracer predicts and traces the null frequency with a RPE (Recursive Prediction Error) algorithm and a Gauss-Newton method. 